Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON):

Solution:
#!/usr/bin/env python3
from __future__ import absolute_import
from sys import stdin, stdout
from itertools import imap

def rint():
    return imap(int, stdin.readline().split())
#lines = stdin.readlines()

def incr(r, n):
    global mnew
    global seqnum
    for i in xrange(c):
            mnew[r][i] += n
    seq.append([u'row ', r+1, n])
    seqnum +=n
def incc(c, n):
    global mnew
    global seqnum
    for i in xrange(r):
        mnew[i][c] += n
    seq.append([u'col ', c+1, n])
    seqnum +=n

r, c = rint()

m = [[] for i in xrange(r)]
for i in xrange(r):
    m[i] = list(rint())

minseqnum = 0
minseq = []
found = 0
for r0 in xrange(501):
    seqnum = 0
    mnew = [[0 for j in xrange(c)] for i in xrange(r)]
    seq = []
    invalid = 0
    if min(m[0]) < r0:
        continue
    incr(0, r0)
    for cc in xrange(0,c):
        adding = m[0][cc] - mnew[0][cc]
        if adding < 0:
            invalid = 1
            break
        incc(cc, m[0][cc] - mnew[0][cc])
    for rr in xrange(1,r):
        if invalid:
            break
        adding = m[rr][0] - mnew[rr][0]
        if adding < 0:
            invalid = 1
            break
        incr(rr, adding)
    if invalid:
        continue
    if m == mnew:
        found = 1
        if minseqnum > seqnum or minseqnum == 0:
            minseq = seq
            minseqnum = seqnum
if found == 0:
    print -1
    exit()
print minseqnum
for ans in minseq:
    for i in xrange(ans[2]):
        print ans[0], ans[1]